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Cutting the bridge down too much can lower the break angle of strings over the saddle though, so it's a slightly bodgey way of doing it.
I'm going to investigate this bolt-on theory. I can see the tip of a threaded rod and a tapped plate on the inside of the heel block, and there's a tell-tale filled-in bolt hole on the outside on the heel block. Will pick away at that and see what's inside.
I just took it apart and gave it a clean. Was filthy. Probably needs another couple of goes. There were used matches as shims under the not-a-nut (it has a zero fret) for some reason. All the tuners seem intact and hopefully will be smooth enough with a scrub and some oil. The fret ends are SHARP and there's a nick in one fret top that's uncomfortable to touch. The neck seems straight, with a tiny amount of relief with the strings off.
Not sure what to do about the action. I've never taken a neck off but am up for trying. But the bridge also seems like a few mm could be taken off the bottom of the top part.